The idea that natural selection can operate on cultural as well as genetic variation is central to recent theories of cultural evolution. This raises an overarching question: how much of traditional evolutionary theory, which was formulated in population-genetic terms, can survive intact once the possibility of cultural inheritance is taken into account? This question is addressed in relation to R. A. Fisher’s “fundamental theorem” of natural selection. Though Fisher’s theorem may appear to be an essentially genetic result, a version of the theorem can be derived that applies to any evolving population, with an arbitrary inheritance mechanism. However, I argue that the biological significance of this “generalized” version of the fundamental theorem is less than that of the Fisherian original